Ball, J. M. (1997) Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations. Journal of Nonlinear Science, 7 (5). pp. 475-502. ISSN 0938-8974 (Paper) 1432-1467 (Online)
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A class of semiflows having possibly nonunique solutions is defined. The measurability and continuity properties of such generalized semiflows are studied. It is shown that a generalized semiflow has a global attractor if and only if it is pointwise dissipative and asymptotically compact. The structure of the global attractor in the presence of a Lyapunov function, and its connectedness and stability properties are studied. In particular, examples are given in which the global attractor is a single point but is not Lyapunov stable.
The existence of a global attractor for the 3D incompressible Navier-Stokes equations is established under the (unproved) hypothesis that all weak solutions are continuous from to .
|Additional Information:||There is a one-page erratum to this paper. http://www.springerlink.com/openurl.asp?genre=article&eissn=1432-1467&volume=8&issue=2&spage=233|
|Subjects:||O - Z > Partial differential equations|
D - G > Dynamical systems and ergodic theory
D - G > Fluid mechanics
|Research Groups:||Oxford Centre for Nonlinear PDE|
|Deposited By:||John Ball|
|Deposited On:||30 Aug 2005|
|Last Modified:||20 Jul 2009 14:19|
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